MthSc 208, Spring 2011 (Differential Equations)Dr. MacauleyHW 1Due Friday January 21st, 2010(1) LetP(t) be the net worth of an investment aftertyears, that is growing at a 5% rate.Suppose that after two years, the investment is worth $200. Write down aninitial valueproblem(the differential equation & initial condition) forP, and sketch its solution.(2) LetT(t) be the temperature of a cup of watertminutes after being placed in a roomwhere the ambient temperature is 72◦.(a) Write down a differential equation thatTsatisfies.(b) Sketch the solution curve of the solution satisfyingT(0) = 100.(c) Sketch the solution curve of the solution satisfyingT(0) = 40.(d) Sketch the solution curve of the solution satisfyingT(0) = 72.(3) Repeat the previous exercise, except letT(t) be the temperature of a sheet of metal (whichcools down and heats upmuchquicker than water). Qualitatively, what is the differencebetween the solution curves in these two problems? Which value ofkis bigger and why?
This is the end of the preview.
access the rest of the document.